Get seats near the front center of the stage. If there are not seats near the front, but just standing room, stand in that area. If you're too far away the performer will not be able to see you and invite you up. Remember to be as close as you can to the performer's spot on the stage. Usually the main performer, such as the lead singer, is near the center of the stage, so try to stand or sit near there.
Learn the words to all the songs. Typically, those who get invited on stage are huge fans of the performer, and one way to show that off is to sing along with every word. Demonstrate your love for the performer by singing along to every song, and that will make you more likely to grab their attention.
Wear clothing that stands out. If you visually stand out in a crowd, that will make it easier for you to get noticed by the performer. Many performers are into fashion and standing out among the crowd, so they appreciate when others share this interest.
Hold up a sign with a message proclaiming your admiration for the performer. They'll notice your sign and might get a kick out of what you wrote. Make it funny and personal. As well, you could flat out say, "Invite me on stage," and that will send a very clear message to the performer. However, try not to make the sign too big or it might anger people behind you.
Yell out for their attention. Many performers don't mind talking to fans during the performance. It's fun for them and the audience. Consider asking, "Invite me on stage!" and they just might do so.